Compound proportion

Feb 2018
63
3
Iran
If 8 workers work 6 hour a day and dig 6 holes of 18 meter depth in 27 days then how many holes of 24 meter depth can 12 workers that work 8 hour a day dig in 12 days?
Please explain step by step
 

skipjack

Forum Staff
Dec 2006
21,481
2,470
If the number of workers is multiplied by 12/8, the number of hours worked per day is multiplied by 8/6, and the number of days worked by each worker is multiplied by 12/27, it seems reasonable to calculate that 12 workers who work 8 hours a day for 12 days can dig 6 × 12/8 × 8/6 × 12/27 holes of 18 meter depth. That 16/3 holes.

If the holes need to be 24 meters deep, instead of 18 meters deep, let's assume that it's necessary to multiply by 18/24. As 16/3 × 18/24 = 4, the final answer is 4.
 
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